Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

Positive solutions for higher order singular p-Laplacian boundary value problems

This paper investigates 2m-th (m ≥ 2) order singular p-Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval.     

Positive solutions for fourth-order singular p -Laplacian boundary value problems

This article investigates fourth-order singular p-Laplacian boundary value problems (BVPs), and obtains the necessary and sufficient conditions for existence of positive solutions for fourth-order singular p-Laplacian BVPs on closed interval.     

Positive solutions for the boundary value problems of one-dimensional p-Laplacian with delay

This paper is concerned with the existence of positive solutions for the boundary value problem of one-dimensional p-Laplacian with delay. The proof is based on the Guo–Krasnoselskii fixed-point theorem in cones.     

Several existence theorems of nonlinear m-point boundary value problem for p-Laplacian dynamic equations on time scales

In this paper, several existence theorems of positive solutions are established for nonlinear m-point boundary value problem for p-Laplacian dynamic equations on time scales, as an application, an example to demonstrate our results is given. The conditions we used in the paper are different from those in [H.R. Sun, W.T. Li, Positive solutions for nonlinear three-point boundary value problems on time scales, J. Math. Anal. Appl. 299 (2004) 508–524; H.R. Sun, W.T. Li, Positive solutions for nonlinear m-point boundary value problems on time scales, Acta Math. Sinica 49 (2006) 369–380 (in Chinese); Y. Wang, C. Hou, Existence of multiple positive solutions for one-dimensional p-Laplacian, J. Math. Anal. Appl. 315 (2006) 144–153; Y. Wang, W. Ge, Positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian, Nonlinear Appl. 66 (6) (2007) 1246–1256].     

Eigenvalue problems for higher-order p-Laplacian dynamic equations on time scales

Let T be a time scale. The existence of positive solutions for the nonlinear four-point singular boundary value eigenvalue problem with higher-order p-Laplacian dynamic equations on time scales is studied. By using the fixed-point index theory, we derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the eigenvalue problem is guaranteed, and the existence of at least two solutions for λ in an appropriate interval is also discussed.     

Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).     

Existence and iteration of positive pseudo-symmetric solutions for a three-point second-order -Laplacian BVP

In this work, we apply a monotone iterative procedure to prove the existence of positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problem.     

The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator

In this paper, we study the existence of countable many positive solutions for a class of nonlinear singular boundary value systems with p-Laplacian operator:

     

Existence and Uniqueness of Positive Solutions of a Kind of Multi-point Boundary Value Problems for Nonlinear Fractional Differential Equations with <Emphasis Type="BoldItalic">p</Emphasis>-Laplacian Operator

In this paper, we investigate the existence and uniqueness of positive solutions of a kind of multi-point boundary value problems for nonlinear fractional differential equations with p-Laplacian operator using the Banach contraction mapping principle. Furthermore, some examples are given to illustrate our results.     

Multiple positive solutions to multipoint one-dimensional <Emphasis Type="Italic">p</Emphasis>-Laplacian boundary value problem with impulsive effects

In this paper, using a fixed point theorem on a convex cone, we consider the existence of positive solutions to the multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects, and obtain multiplicity results for positive solutions.     

Triple positive solutions for a class of -point dynamic equations on time scales with -Laplacian

This paper deals with a class of second-order nonlinear m-point dynamic equation on time scales with one-dimensional p-Laplacian. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order delta derivative explicitly. Meanwhile, an example is worked out to demonstrate the main results.     

Ground state periodic solutions for difference equations with discrete p-Laplacian

We use the critical point theory to establish existence results for periodic solutions of some nonlinear boundary value problems involving the discrete p-Laplacian operator. As an application we give an alternative proof to the upper and lower solutions theorem.     

Positive solution of three-point boundary value problem for the one-dimensional p-Laplacian with singularities

In the paper, we deal with positive solutions of the following nonlinear three-point singular boundary value problem with a p-Laplacian operator:

     

Positive solutions for a fractional boundary value problem with p-Laplacian operator

In this paper, we are mainly concerned with positive solutions for a p-Laplacian fractional boundary value problem. By virtue of Jensen’s inequalities and some new properties of the Green function of the problem, we adopt the Krasnoselskii-Zabreiko fixed point theorem to establish the results of existence and multiplicity of the positive solutions. Finally, a uniqueness theorem is established by using a fixed point theorem of concave operator and an example is given to illustrate the result.     

Three positive solutions for the one-dimensional p-Laplacian

In this paper, nonlinear two point boundary value problems with p-Laplacian operators subject to Dirichlet boundary condition and nonlinear boundary conditions are studied. We show the existence of three positive solutions by the five functionals fixed point theorem.     

Existence of solutions for fractional impulsive differential equations with p-Laplacian operator

We investigate the boundary value problems for nonlinear fractional impulsive differential equations with p-Laplacian operator. By applying some standard fixed point theorems, we obtain new results on the existence and uniqueness of solutions. Examples are given to show the applicability of our results.     

Asymptotic properties of singular solutions in degenerate parabolic equation with boundary flux

ABSTRACT

This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively.     

A note on the existence of positive solutions of one-dimensional <Emphasis Type="Italic">p</Emphasis>-Laplacian boundary value problems

This paper is concerned with the existence of positive solutions of a multipoint boundary value problem for higher-order differential equation with one-dimensional p-Laplacian. Examples are presented to illustrate the main results. The result in this paper generalizes those in existing papers.     

Existence of positive solutions for Sturm-Liouville-like boundary value problem with p-Laplacian on time scales

We consider the existence of positive solutions for a class of Sturm-Liouville-like boundary value problem with p-Laplacian on time scales. Using the well known Krasnosel’ski’s fixed point theorem, some new existence criteria for positive solutions of the boundary value problem are presented. As an application, two examples are given to illustrate the main results.